scholarly journals Nonrelativistic near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills with SU(1, 1) symmetry

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Stefano Baiguera ◽  
Troels Harmark ◽  
Nico Wintergerst
Keyword(s):  
Classical Limit ◽  
Particle Number ◽  
Matrix Theory ◽  
Companion Paper ◽  
Positive Definite ◽  
Normal Ordering ◽  
Yang Mills ◽  
Three Sphere ◽  
Dilatation Operator ◽  
Definite Expressions

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super Yang-Mills (SYM) theory that approach BPS bounds and for which an SU(1,1) structure is preserved. The resulting near-BPS theories become non-relativistic, with a U(1) symmetry emerging in the limit that implies the conservation of particle number. They are obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and subsequently integrating out fields that become non-dynamical as the bounds are approached. Upon quantization, and taking into account normal-ordering, they are consistent with taking the appropriate limits of the dilatation operator directly, thereby corresponding to Spin Matrix theories, found previously in the literature. In the particular case of the SU(1,1—1) near-BPS/Spin Matrix theory, we find a superfield formulation that applies to the full interacting theory. Moreover, for all the theories we find tantalizingly simple semi-local formulations as theories living on a circle. Finally, we find positive-definite expressions for the interactions in the classical limit for all the theories, which can be used to explore their strong coupling limits. This paper will have a companion paper in which we explore BPS bounds for which a SU(2,1) structure is preserved.

scholarly journals Symmetry structure of the interactions in near-BPS corners of $$ \mathcal{N} $$ = 4 super-Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Stefano Baiguera ◽  
Troels Harmark ◽  
Yang Lei ◽  
Nico Wintergerst
Keyword(s):  
Irreducible Representation ◽  
Classical Limit ◽  
Positive Definiteness ◽  
Yang Mills ◽  
Three Sphere ◽  
Effective Dynamics ◽  
Coupling Dynamics ◽  
Full Interaction ◽  
Interaction Term ◽  
Symmetry Structure

Abstract We consider limits of $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory that approach BPS bounds. These limits result in non-relativistic near-BPS theories that describe the effective dynamics near the BPS bounds and upon quantization are known as Spin Matrix theories. The near-BPS theories can be obtained by reducing $$ \mathcal{N} $$ N = 4 SYM on a three-sphere and integrating out the fields that become non-dynamical in the limits. We perform the sphere reduction for the near-BPS limit with SU(1, 2|2) symmetry, which has several new features compared to the previously considered cases with SU(1) symmetry, including a dynamical gauge field. We discover a new structure in the classical limit of the interaction term. We show that the interaction term is built from certain blocks that comprise an irreducible representation of the SU(1, 2|2) algebra. Moreover, the full interaction term can be interpreted as a norm in the linear space of this representation, explaining its features including the positive definiteness. This means one can think of the interaction term as a distance squared from saturating the BPS bound. The SU(1, 1|1) near-BPS theory, and its subcases, is seen to inherit these features. These observations point to a way to solve the strong coupling dynamics of these near-BPS theories.

scholarly journals The integrable (hyper)eclectic spin chain

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Changrim Ahn ◽  
Matthias Staudacher
Keyword(s):  
Spin Chain ◽  
Nearest Neighbor ◽  
Inverse Scattering Method ◽  
Spin Chains ◽  
Scattering Method ◽  
Yang Mills ◽  
Deformation Parameters ◽  
Dilatation Operator ◽  
The One ◽  
State Spin

Abstract We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of $$ \mathcal{N} $$ N = 4 Super Yang-Mills Theory.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

scholarly journals Asymptotic dynamics on the worldline for spinning particles

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Domenico Bonocore
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Boson ◽  
Classical Limit ◽  
Wilson Line ◽  
Background Field ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Yang Mills ◽  
Asymptotic Dynamics ◽  
Gravity Theories

Abstract There has been a renewed interest in the description of dressed asymptotic states à la Faddeev-Kulish. In this regard, a worldline representation for asymptotic states dressed by radiation at subleading power in the soft expansion, known as the Generalized Wilson Line (GWL) in the literature, has been available for some time, and it recently found applications in the derivation of factorization theorems for scattering processes of phenomenological relevance. In this paper we revisit the derivation of the GWL in the light of the well-known supersymmetric wordline formalism for the relativistic spinning particle. In particular, we discuss the importance of wordline supersymmetry to understand the contribution of the soft background field to the asymptotic dynamics. We also provide a derivation of the GWL for the gluon case, which was not previously available in the literature, thus extending the exponentiation of next-to-soft gauge boson corrections to Yang-Mills theory. Finally, we comment about possible applications in the current research about asymptotic states in scattering amplitudes for gauge and gravity theories and their classical limit.

scholarly journals Dilatation operator in (super-)Yang–Mills theories on the light-cone

2005 ◽  
Vol 708 (1-3) ◽  
pp. 115-193 ◽  
Author(s):  
A.V. Belitsky ◽  
S.É. Derkachov ◽  
G.P. Korchemsky ◽  
A.N. Manashov
Keyword(s):  
Light Cone ◽  
Yang Mills ◽  
Dilatation Operator

scholarly journals TOWARDS THE LOCALIZATION OF SUSY GAUGE THEORY ON A CURVED SPACE

2012 ◽  
Vol 27 (06) ◽  
pp. 1250029 ◽  
Author(s):  
KOICHI NAGASAKI ◽  
SATOSHI YAMAGUCHI
Keyword(s):  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Path Integral ◽  
General Class ◽  
Positive Definite ◽  
Curved Space ◽  
Yang Mills ◽  
Curved Spaces ◽  
Supersymmetric Gauge ◽  
Exact Term

We consider an [Formula: see text] supersymmetric gauge theory on a curved space. We try to generalize Pestun's localization calculation on the four-sphere to a more general class of curved spaces. We calculated the Q-exact term to localize the path-integral, and when it becomes positive-definite, we obtain a configuration where the path-integral localizes. We also evaluate the super-Yang–Mills action in this configuration.

scholarly journals Glueball spectra from a matrix model of pure Yang–Mills theory

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Nirmalendu Acharyya ◽  
A. P. Balachandran ◽  
Mahul Pandey ◽  
Sambuddha Sanyal ◽  
Sachindeo Vaidya
Keyword(s):  
Renormalization Group ◽  
Excellent Agreement ◽  
Matrix Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Yang Mills ◽  
Three Sphere ◽  
Simple Matrix

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang–Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang–Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

Sign in / Sign up

Export Citation Format

Share Document